I just had issues with the same oil pressure switch.
How this works is it’s a 3 terminal on/off/on switch with two power leads coming in, and the other going to the fuel pump. One is hooked to the starter solenoid and is only provides power to the fuel pump when the starter is engaged.the other power line is switched on when the switch detects oil pressure and stays on as long as the engine is running. If the engine dies for any reason the fuel pump shuts off…. That is the way it’s designed to work for safety reasons. If you have power to your fuel pump when you turn on the key , your wiring is wrong, and it’s dangerous…. Kirk